Unified theoretical framework for polycrystalline pattern evolution

Grain rotation mechanisms in nanocrystalline materials: Multiscale observations in Pt thin films

Near-rigid-body grain rotation is commonly observed during grain growth, recrystallization, and plastic deformation in nanocrystalline materials. Despite decades of research, the dominant mechanisms underlying grain rotation remain enigmatic. We present direct evidence that grain rotation occurs through the motion of disconnections (line defects with step and dislocation character) along grain boundaries in platinum thin films. State-of-the-art in situ four-dimensional scanning transmission electron microscopy (4D-STEM) observations reveal the statistical correlation between grain rotation and grain growth or shrinkage. This correlation arises from shear-coupled grain boundary migration, which occurs through the motion of disconnections, as demonstrated by in situ high-angle annular dark-field STEM observations and the atomistic simulation-aided analysis. These findings provide quantitative insights into the structural dynamics of nanocrystalline materials.

Disconnection flow-mediated grain rotation

Grain rotation is commonly observed during the evolution of microstructures in polycrystalline materials of different kinds, including metals, ceramics, and colloidal crystals. It is widely accepted that interface migration in these systems is mediated by the motion of line defects with step and dislocation character, i.e., disconnections. We propose a crystallography-respecting continuum model for arbitrarily curved grain boundaries or heterophase interfaces, accounting for the disconnections' role in grain rotation. Numerical simulations demonstrate that changes in grain orientations, as well as interface morphology and internal stress field, are associated with disconnection flow. Our predictions agree with molecular dynamics simulation results for pure capillarity-driven evolution of grain boundaries and are interpreted through an extended Cahn-Taylor model.

Shear-assisted grain coarsening in colloidal polycrystals

Grain growth under shear annealing is crucial for controlling the properties of polycrystalline materials. However, their microscopic kinetics are not well understood because individual atomic trajectories are difficult to track. Here, we study grain growth with single-particle kinetics in colloidal polycrystals using video microscopy. Rich grain-growth phenomena are revealed in three shear regimes, including the normal grain growth (NGG) in weak shear melting-recrystallization process in strong shear. For intermediate shear, early stage NGG is arrested by built-up stress and eventually gives way to dynamic abnormal grain growth (DAGG). We find that DAGG occurs via a melting-recrystallization process, which naturally explains the puzzling stress drop at the onset of DAGG in metals. Moreover, we visualize that grain boundary (GB) migration is coupled with shear via disconnection gliding. The disconnection-gliding dynamics and the collective motions of ambient particles are resolved. We also observed that grain rotation can violate the conventional relation [Formula: see text] (R is the grain radius, and θ is the misorientation angle between two grains) by emission and annihilation of dislocations across the grain, resulting in a step-by-step rotation. Besides grain growth, we discover a result in shear-induced melting: The melting volume fraction varies sinusoidally on the angle mismatch between the triangular lattice orientation of the grain and the shear direction. These discoveries hold potential to inform microstructure engineering of polycrystalline materials.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

The ordering kinetics of standing cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers (molecular weight: 39 kg mol^-1) close to the order-disorder transition is experimentally investigated following the temporal evolution of the correlation length at different annealing temperatures. The growth exponent of the grain-coarsening process is determined to be 1/2, signature of a curvature-driven ordering mechanism. The measured activation enthalpy and the resulting Meyer-Neldel temperature for this specific copolymer along with the data already known for PS-b-PMMA block copolymers in strong segregation limit allow investigation of the interplay between the ordering kinetics and the thermodynamic driving force during the grain coarsening. These findings unveil various phenomena concomitantly occurring during the thermally activated ordering kinetics at segmental, single chain, and collective levels.

Competing factors in grain boundary loop shrinkage: Two-dimensional hard sphere colloidal crystals

A grain boundary (GB) loop in a two-dimensional solid is the boundary of a domain or grain whose lattice orientation is mismatched with its uniform surroundings. Understanding the factors that influence the rate at which the interior of a GB loop relaxes to the orientation of its surroundings is an important step toward control and predictability of grain coarsening in general. Recent computational and experimental studies looking at the rate of GB loop shrinkage in two-dimensional colloidal hard sphere solids have uncovered contradictory trends: in experiments, GB loops with low misorientation angles shrank the fastest, while in simulations, they persisted the longest. In this study, the computational system's behavior is brought into qualitative agreement with the experimental results through increasing the lateral packing pressure, decreasing the domain size, and mimicking the experimental protocol used to form the GB loop. Small GB loops with the same misorientation, but displaying either a hexagonal or starlike grain shape depending on the orientation of their six dislocations, are shown to differ in their rates of shrinkage by two orders of magnitude. The evidence suggests that both the barrier to generating new dislocations as well as the pattern of dislocations formed by different GB loop preparation methods will determine which trend is observed.

Separation of Elastic and Plastic Timescales in a Phase Field Crystal Model

A consistent small-scale description of plasticity and dislocation motion in a crystalline solid is presented based on the phase field crystal description. By allowing for independent mass motion and lattice distortion, the crystal can maintain elastic equilibrium on the timescale of plastic motion. We show that the singular (incompatible) strains are determined by the phase field crystal density, while the smooth distortions are constrained to satisfy elastic equilibrium. A numerical implementation of the model is presented and used to study a benchmark problem: the motion of an edge dislocation dipole in a triangular lattice. The time dependence of the dipole separation agrees with continuum elasticity with no adjustable parameters.

A Study of Strain-Driven Nucleation and Extension of Deformed Grain: Phase Field Crystal and Continuum Modeling

The phase-field-crystal (PFC) method is used to investigate migration of grain boundary dislocation and dynamic of strain-driven nucleation and growth of deformed grain in two dimensions. The simulated results show that the deformed grain nucleates through forming a gap with higher strain energy between the two sub-grain boundaries (SGB) which is split from grain boundary (GB) under applied biaxial strain, and results in the formation of high-density ensembles of cooperative dislocation movement (CDM) that is capable of plastic flow localization (deformed band), which is related to the change of the crystal lattice orientation due to instability of the orientation. The deformed grain stores the strain energy through collective climbing of the dislocation, as well as changing the orientation of the original grain. The deformed grain growth (DGG) is such that the higher strain energy region extends to the lower strain energy region, and its area increase is proportional to the time square. The rule of the time square of the DGG can also be deduced by establishing the dynamic equation of the dislocation of the strain-driven SGB. The copper metal is taken as an example of the calculation, and the obtained result is a good agreement with that of the experiment.

Dislocation-controlled formation and kinetics of grain boundary loops in two-dimensional crystals

The formation and kinetics of grain boundaries are closely related to the topological constraints imposed on their complex dislocation structure. Loop-shaped grain boundaries are unique structures to establish such a link because their overall topological "charge" is zero due to their null net Burgers vector. Here, we observe that a local rotational deformation of a 2D colloidal crystal with an optical vortex results in a grain boundary loop only if the product of its radius and misorientation exceeds a critical value. Above this value, the deformation is plastic and the grain boundary loop spontaneously shrinks at a rate that solely depends on this product, while otherwise, the deformation is elastically restored. We show that this elastic-to-plastic crossover is a direct consequence of the unique dislocation structure of grain boundary loops. At the critical value, the loop is structurally equivalent to the so-called "flower defect" and the shrinkage rate diverges. Our results thus reveal a general limit on the formation of grain boundary loops in 2D crystals and elucidate the central role of defects in both the onset of plasticity and the kinetics of grain boundaries.

Grain Boundary Structures and Collective Dynamics of Inversion Domains in Binary Two-Dimensional Materials

Understanding and controlling the properties and dynamics of topological defects is a lasting challenge in the study of two-dimensional materials, and is crucial to achieve high-quality films required for technological applications. Here grain boundary structures, energies, and dynamics of binary two-dimensional materials are investigated through the development of a phase field crystal model that is parametrized to match the ordering, symmetry, energy, and length scales of hexagonal boron nitride. Our studies reveal some new dislocation core structures for various symmetrically and asymmetrically tilted grain boundaries, in addition to those obtained in previous experiments and first-principles calculations. We also identify a defect-mediated growth dynamics for inversion domains governed by the collective atomic migration and defect core transformation at grain boundaries and junctions, a process that is related to inversion symmetry breaking in binary lattice.

Hydrodynamic theory of freezing: Nucleation and polycrystalline growth

Structural aspects of crystal nucleation in undercooled liquids are explored using a nonlinear hydrodynamic theory of crystallization proposed recently [G. I. Tóth et al., J. Phys.: Condens. Matter 26, 055001 (2014)JCOMEL0953-898410.1088/0953-8984/26/5/055001], which is based on combining fluctuating hydrodynamics with the phase-field crystal theory. We show that in this hydrodynamic approach not only homogeneous and heterogeneous nucleation processes are accessible, but also growth front nucleation, which leads to the formation of new (differently oriented) grains at the solid-liquid front in highly undercooled systems. Formation of dislocations at the solid-liquid interface and interference of density waves ahead of the crystallization front are responsible for the appearance of the new orientations at the growth front that lead to spherulite-like nanostructures.

Emergence of Chirality from Isotropic Interactions of Three Length Scales

Chirality is known to play a pivotal role in determining material properties and functionalities. However, it remains a great challenge to understand and control the emergence of chirality and the related enantioselective process particularly when the building components of the system are achiral. Here we explore the generic mechanisms driving the formation of two-dimensional chiral structures in systems characterized by isotropic interactions and three competing length scales. We demonstrate that starting from isotropic and rotationally invariant interactions, a variety of chiral ordered patterns and superlattices with anisotropic but achiral units can self-assemble. The mechanisms for selecting specific states are related to the length-scale coupling and the selection of resonant density wave vectors. Sample phase diagrams and chiral elastic properties are identified. These findings provide a viable route for predicting chiral phases and selecting the desired handedness.

Long-wavelength properties of phase-field-crystal models with second-order dynamics

The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.

Consistent Hydrodynamics for Phase Field Crystals

We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.

Hexagonal phase ordering in strongly segregated copolymer films

Strongly segregated copolymer mixtures with uneven composition ratio can form hexagonally ordered thin films. A simplified model describing the size and position of micellelike clusters is derived, allowing for investigation of much larger domain sizes than in previous studies. Simulations of this model are performed to study the generation of large scale order and evolution of pattern defects. We find three temporal regimes exhibiting different scaling laws for orientational correlation length and defect number. In the early stage, topological defects are rapidly eliminated by pairwise annihilation. A slower intermediate stage is characterized by the migration of grain boundaries and the elimination of small grains. In the final stage, grain boundaries become pinned and the evolution halts. A scaling law for defect interaction is proposed which is consistent with the crossover between the first and second stages.

Rotation-limited growth of three-dimensional body-centered-cubic crystals

According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered-cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe, as a function of the quenching depth, a crossover between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of -1.25. The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations.

Morphological instability of grain boundaries in two-phase coherent solids

We show both computationally and analytically that grain boundaries that exhibit shear-coupled motion become morphologically unstable in solid alloys that phase separate into coherent domains of distinct chemical compositions. We carry out simulations of continuum models demonstrating that this instability is mediated by long-range elastic interaction between compositional domains and grain boundaries. In addition, we perform a linear stability analysis that predicts the range of unstable wavelengths in good quantitative agreement with simulations. In nonlinear stages, this pattern-forming instability leads to the breakup of low-angle grain boundaries, thereby strongly impacting microstructural evolution in a wide range of phase-separating materials.

Crystallization induced by multiple seeds: dynamical density functional approach

Using microscopic dynamical density functional theory, we calculate the dynamical formation of polycrystals by following the crystal growth around multiple crystalline seeds imposed to an undercooled fluid. Depending on the undercooling and the size ratio as well as the relative crystal orientation of two neighboring seeds, three possibilities of the final state emerge, namely no crystallization at all, formation of a monocrystal, or two crystallites separated by a curved grain boundary. Our results, which are obtained for two-dimensional hard disk systems using a fundamental-measure density functional, shed new light on the particle-resolved structure and growth of polycrystalline material in general.